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We consider the inverse problem to determine the shape of an insulated inclusion within a heat conducting medium from overdetermined Cauchy data of solutions for the heat equation on the accessible exterior boundary of the medium. For the approximate solution of this ill-posed and nonlinear problem we propose a regularized Newton iteration scheme based on a… (More)

- Roman Chapko
- Mathematics and Computers in Simulation
- 2004

- Roman Chapko
- 2016 IEEE International Conference on…
- 2016

We consider two types of inverse boundary problems related to the Laplace equation in planar double connected domains. The first one consists in the determining the Cauchy data on an inclusion from given Cauchy data on an accessible exterior boundary. On this accessible part the function (or the normal derivative) is known and, additionally, on a portion of… (More)

- Roman Chapko, Christina Babenko, Volodymyr Khlobystov, Volodymyr Makarov
- Int. J. Comput. Math.
- 2014

- Roman Chapko, B. Tomas Johansson, V. Vavrychuk
- Mathematics and Computers in Simulation
- 2014

- Roman Chapko, B. Tomas Johansson, Olena Protsyuk
- Int. J. Comput. Math.
- 2012

- Roman Chapko, Rainer Kress, Lars Mm Onch
- 2007

In this paper we describe a fully discrete quadrature method for the numerical solution of a hypersingular integral equation of the rst kind for the scattering of time-harmonic elastic waves by a cavity crack. We establish convergence of the method and prove error estimates in a HH older space setting. Numerical examples illustrate the convergence results.

- Roman Chapko, Rainer Kress
- 2007

- Roman Chapko
- Applied Mathematics and Computation
- 2004

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